Longitudinal data can be used to estimate transition intensities between healthy and unhealthy states prior to death. When health is defined with respect to cognitive ability during old age, the trajectory of performance is either static or downward. An illness-death model is presented where the intensity of a transition is allowed to change over time by using a piecewise-constant model or by using a Weibull model. Observed improvement of cognitive ability is modelled as misclassification. The methodology is extended to estimate life expectancy with and without cognitive impairment. The measurement of cognitive ability is important as it is an important predictor of future need for care. The models can help to understand how cognitive decline develops over time and which factors play a role. The methods are illustrated using data from the Medical Research Council Cognitive Function and Ageing Study in the U.K. (1991-2005).